Efficiency and Implementation Security of Code-based Cryptosystems

This thesis studies efficiency and security problems of implementations of code-based cryptosystems. These cryptosystems, though not currently used in the field, are of great scientific interest, since no quantum algorithm is known that breaks them essentially faster than any known classical algorithm. This qualifies them as cryptographic schemes for the quantum-computer era, where the currently used cryptographic schemes are rendered insecure. Concerning the efficiency of these schemes, we propose a solution for the handling of the public keys, which are, compared to the currently used schemes, of an enormous size. Here, the focus lies on resource-constrained devices, which are not capable of storing a code-based public key of communication partner in their volatile memory. Furthermore, we show a solution for the decryption without the parity check matrix with a passable speed penalty. This is also of great importance, since this matrix is of a size that is comparable to that of the public key. Thus, the employment of this matrix on memory-constrained devices is not possible or incurs a large cost. Subsequently, we present an analysis of improvements to the generally most time-consuming part of the decryption operation, which is the determination of the roots of the error locator polynomial. We compare a number of known algorithmic variants and new combinations thereof in terms of running time and memory demands. Though the speed of pure software implementations must be seen as one of the strong sides of code-based schemes, the optimisation of their running time on resource-constrained devices and servers is of great relevance. The second essential part of the thesis studies the side channel security of these schemes. A side channel vulnerability is given when an attacker is able to retrieve information about the secrets involved in a cryptographic operation by measuring physical quantities such as the running time or the power consumption during that operation. Specifically, we consider attacks on the decryption operation, which either target the message or the secret key. In most cases, concrete countermeasures are proposed and evaluated. In this context, we show a number of timing vulnerabilities that are linked to the algorithmic variants for the root-finding of the error locator polynomial mentioned above. Furthermore, we show a timing attack against a vulnerability in the Extended Euclidean Algorithm that is used to solve the so-called key equation during the decryption operation, which aims at the recovery of the message. We also present a related practical power analysis attack. Concluding, we present a practical timing attack that targets the secret key, which is based on the combination of three vulnerabilities, located within the syndrome inversion, a further suboperation of the decryption, and the already mentioned solving of the key equation. We compare the attacks that aim at the recovery of the message with the analogous attacks against the RSA cryptosystem and derive a general methodology for the discovery of the underlying vulnerabilities in cryptosystems with specific properties. Furthermore, we present two implementations of the code-based McEliece cryptosystem: a smart card implementation and flexible implementation, which is based on a previous open-source implementation. The previously existing open-source implementation was extended to be platform independent and optimised for resource-constrained devices. In addition, we added all algorithmic variants presented in this thesis, and we present all relevant performance data such as running time, code size and memory consumption for these variants on an embedded platform. Moreover, we implemented all side channel countermeasures developed in this work. Concluding, we present open research questions, which will become relevant once efficient and secure implementations of code-based cryptosystems are evaluated by the industry for an actual application.